*Visnyk LNAU: Architecture and Farm Building 2018 №19: 10-18*

## RIGIDITIES OF IRON-CONCRETE CROSS-SECTIONS AND ANALYSIS OF THE BEAMS TAKING INTO CONSIDERATION PHYSICAL NONLINEARITIES

**T. Janiak**, Candidate of Technical Sciences

University of Technology and Life Sciences in Bydgoszcz

**S. Burchenya**, Candidate of Technical Sciences

Lviv National Agrarian University

https://doi.org/10.31734/architecture2018.19.010
#### Annotation

The thesis presents an original algorithm for calculating the rigidity for bending of reinforced concrete cross-sections as well as examples for using the function of rigidity when conducting a statistical analysis of a beam. The functions of rigidity were calculated with longitudinal reinforcement taken into consideration and assuming the material nonlinearity. It was decided to use the physical relationships set in the Eurocode 2 (EC2). Because of that the terminology, used in this standard, has also been used in the body of text.

Eurocode 2 sets two different strain-deformation dependencies. The first one is recommended in nonlinear structures and the other one when dimensioning reinforced concrete cross-sections

Physical-mechanical properties of reinforcement steel are more homogenous than these of concrete.

The developed calculation algorithm of reinforced concrete beams consists of two main phases. The first chase involves an analysis of reinforce concrete beams used in further calculations. It ends with determining a rigidity function for each distinctive cross-section. These functions are then used in the second phase when a nonlinear static beam analysis is performed.

The first stage of algorithm is based on the principles laid out in EC2.

The second stage of calculation includes numerical static analysis of the beam. For this purpose a classic MRS algorithm calculating beams with changing rigidity was used. The calculations are relatively simple when using the iteration formula.

The thesis presents three example calculations prepared using the aforementioned algorithm. The first pertains to a single concrete cross-section and an analysis of the concrete durability class's influence on the form of the function as well as rigidity function's influence on bending. Another two examples involve linear and nonlinear static analysis of two reinforced concrete beams. Particularly interesting results were obtained in case of a beam which had one elastic support. Based on these finding one of the final conclusions was formulated, stating that a precise nonlinear analysis has a significant influence on the calculation results of systems on non-fixed support (including those on elastic surface) as well as mixed structures such as steel and reinforced concrete structures.

#### Key words

rigidities, cross-sections, Eurocode 2, physical nonlinearities

#### Link

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- PN-EN 1992-1-1: 2008. Eurocode 2. Design of concrete structures. Part 1-1: General rules and rules for buildings.
- Janiak T., Niespodziana A., Grabowski A. Analysis of stiffness of bending reinforced concrete sections with the use of non-linear constitutive relations - numerical algorithm. Building Materials. 2013. No. 12. Р. 71-73.